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Direct observation of impurity segregation at dislocation cores in an ionic crystal Eita Tochigi, Yuki Kezuka, Akiho Nakamura, Atsutomo Nakamura, Naoya Shibata, and Yuichi Ikuhara Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b00115 • Publication Date (Web): 13 Apr 2017 Downloaded from http://pubs.acs.org on April 16, 2017
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Direct observation of impurity segregation at dislocation cores in an ionic crystal Eita Tochigi*,†, Yuki Kezuka†, Akiho Nakamura†, Atsutomo Nakamura‡, Naoya Shibata† and Yuichi Ikuhara†,§,ǁ
†
Institute of Engineering Innovation, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 1138656, Japan
‡
Department of Materials Science and Engineering, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
§
Nanostructures Research Laboratory, Japan Fine Ceramics Center 2-4-1, Mutsuno, Atsuta-ku, Nagoya, Aichi 456-8587, Japan ǁ
Center for Elements Strategy Initiative for Structural Materials, Kyoto University, Kyoto 606-8501, Japan.
ABSTRACT: Dislocations—one-dimensional lattice defects—are known to strongly interact with impurity atoms in a crystal. This interaction is generally explained on the basis of the long-range strain field of the dislocation. In ionic crystals, the impurity-dislocation interactions must be influenced by the electrostatic effect in addition to the strain effect. However, such interactions have not been verified yet. Here, we show a direct evidence of the electrostatic impurity-dislocation interaction in α-Al2O3 by visualizing the dopant atom distributions at dislocation cores using atomic-resolution scanning transmission electron microscopy (STEM). It was found that the dopant segregation behaviors strongly depend on the kind of elements, and their valence states are considered to be a critical factor. The observed segregation behaviors cannot be explained by the elastic interactions only, but can be successfully understood if the electrostatic interactions are taken into account. The present findings will ACS Paragon Plus Environment
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lead to the precise and quantitative understanding of impurity induced dislocation properties in many materials and devices. Keywords: Dislocations, segregation, alumina (α-Al2O3), scanning transmission electron microscopy (STEM)
It is well recognized that the impurity atmospheres around a dislocation strongly affect the mechanical properties of crystals as a result of retarding dislocation motion1. In recent years, it has been demonstrated that dislocations often acquire characteristic functional properties, such as electrical conductivity2,3 and magnetism4. To enhance such functional properties, impurity doping into dislocations is a key technique2,3. Impurity distributions around a dislocation have been mainly explained by an elastic interaction owing to its long-range strain field based on the linear elasticity theory (as is often called Cottrell effect5). This theory, however, breaks down in the dislocation core region (< b ~ 5b, where b means the magnitude of Burgers vector). In this region impurity distributions are still not well understood because modeling of dislocation cores is too difficult by classical theories and even by modern computational calculations especially for complex compound crystals. In addition, very few experimental results have been reported to show impurity distributions around dislocation cores at the atomic level, although several experimental studies revealed the presence of impurity atmospheres around dislocations in metals6 or semiconductors7. In ionic crystals, it has long been considered that dislocations can have an extra electrical charge owing to a local deviation from stoichiometry8, and the charged dislocations are expected to accompany electrostatic fields. If this is the case, the electrostatic interaction between impurities and dislocation cores should be considered in addition to the elastic interaction. However there have been no direct evidences for the electrostatic interaction in ionic crystals. In recent years, atomic-scale direct ACS Paragon Plus Environment
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-
-
observations have shown that partial dislocations with the Burgers vector of 1/3 and 1/3 -
dissociated from the 1/3 edge dislocation in α-Al2O3 have nonstoichiometric cores9. This system may be a good model system to investigate the electrostatic interactions between dislocation cores and impurities. In this study, we systematically doped five different types of impurities (Ni, Sr, Er, Ti, and -
-
-
Zr) to the {1120}/ low-angle tilt grain boundary of α-Al2O3, which is consisted of the 1/3 -
-
and 1/3 partial-dislocation pairs dissociated from the 1/3 edge dislocations10. The dopant distributions around the partial dislocations were directly observed by atomic-resolution STEM. It was found that the doped impurities do segregate to the dislocation cores, but the segregation structures are strongly influenced by the kinds of elements, especially on their valence state. These peculiar segregation structures suggest the importance of electrostatic interactions between dislocation cores and impurities in ionic crystals. -
High-purity α-Al2O3 single crystals with mirror finished {1120} faces inclined by 1o from the [0001] direction (>99.99%, Shinkosha Co. Ltd,) were used for the starting materials. Dopants of -
metallic solids (Ni, Sr, Er, Ti, and Zr) were deposited on the {1120} face of the crystals by vacuum evaporation method (for Ni, Sr, Ti, and Zr) or by an argon ion spattering method (for Er). The thickness of the metal layers of Ni, Sr, Ti, and Zr was expected to be a few nm. The thickness of the Er layer was estimated to be 10 Å using a quartz crystal thickness monitor. By joining the metal-deposited crystal and -
-
a pure crystal at 1500oC for 10 h in air, bicrystals with a metal-doped {1120}/ 2o low-angle tilt grain boundary were obtained. Since the bicrystals were joined in air, all the dopants should have the stable valence states in the oxidizing condition (i.e., Ni2+, Sr2+, Er3+, Ti4+, and Zr4+). The atomic numbers, valence states, and effective ionic radii of these dopants are listed in Table 111. The bicrystals were cut with diamond saw and then mechanically grinded to obtain a mirror surface with diamond slurries of 9, 3, and 1 µm grains. After the samples were supported by a molybdenum mesh, they were further grinded to a thickness of about 20 µm. Argon ion milling (Ar+: 4 kV ~ 1 kV) was carried out to make the sample ACS Paragon Plus Environment
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with electron transparency. The resultant boundaries were analyzed by high-angle annular dark-field (HAADF) STEM (JEOL JEM-2100F with a CEOS Cs-corrector operated at 200 kV for the undoped, Ni2+, Sr2+, Er3+, and Zr4+-doped samples and JEOL ARM-200F operated at 200 kV for the Ti4+-doped sample). -
Figure 1a illustrates a rigid model of the 1/3 basal edge dislocation. It has been well -
characterized that the basal edge dislocation has an extended structure consisting of the 1/3 and -
the 1/3 partial dislocations by climb mechanism9, 12-15. The partial dislocations lie on different -
slip planes with the {112 0} stacking fault in between, where the extra-half plane of each partial dislocation is located above each core. We define these two partial dislocations as the upper and lower partials as shown in Figure 1a. Three model structures can be proposed for the partial dislocation cores in terms of the terminating atomic columns (Figure 1b-1d), because the stacking sequence of atomic planes along the [0001] direction is O-Al-Al. We call these three core models as (b) O-core, (c) Al1-core, and (d) Al2-core. From the crystal structure of α-Al2O3, Al1-core is stoichiometric, whereas O-core and Al2-core are nonstoichiometric. Since the perfect dislocation is to preserve total stoichiometry, the possible combinations of the core structures for the upper and lower partial pair are either O-Al2, Al1-Al1, or Al2-O. Previous atomic-resolution (S)TEM studies independently reported conflicting results on the basal dislocation cores: the Al1-Al1 pair model13, 15 and the Al2-O pair model9. Although the atomic-scale basal dislocation core structures are thus still under controversy, the impurity segregation behavior may offer additional information on the determination of the core structures in α-Al2O3. Figure 2a-2f show typical HAADF STEM images of undoped and doped basal dislocation cores. In HAADF STEM, atomic columns are imaged as a bright contrast that is approximately proportional to Z2 (Z: atomic number)16. The zigzag contrasts along the vertical direction in the bulk correspond to the zigzag arrangement of aluminum and oxygen ions as shown by the structure model in Figure 2a. The core positions of the dislocations were determined by a Fourier filtering method (Supplementary ACS Paragon Plus Environment
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Discussion 1) and are indicated by the yellow arrows. As can be seen, the basal dislocations are dissociated into two partial dislocations. The partial dislocation cores are imaged rather dark in the undoped sample (Figure 2a). In doped samples (Figure 2b-2f), the brighter contrasts in the vicinity of the partial dislocation cores directly highlight the segregated dopants. The blue and red profiles show the image-intensity profiles along the horizontal directions indicated by the blue and red triangles at the right-hand side of the images, respectively. The intensity peaks around the dislocation cores are clearly seen in all the graphs except for that of the undoped sample. This demonstrates that all the kinds of dopants segregate to the basal dislocation in α-Al2O3. It is noted that the dopant distributions around the upper and lower partials are not uniform, and strongly dependent on the kinds of elements. In the Sr2+doped case (Figure 2b), the dopant segregation occurs at the upper partial but not at the lower partial. In contrast, in the Ti4+ case (Figure 2f), only the lower partial has some dopants. In the Er3+- and Zr4+doped cases (Figure 2d and 2e) the lower partials have relatively strong segregation than the upper partials. In the Ni2+-doped case (Figure 2c), the two partials have less difference in dopant distributions as compared with the other cases. -
-
It should be mentioned that the 1/3 and 1/3 partial dislocations have the same -
-
edge component of 1/6 and antiparallel screw components of ±1/6. The partial-
-
dislocation pair has two possible configurations: the combination of 1/3 and 1/3 or of -
-
1/3 and 1/3 for the upper and the lower partial dislocations, respectively. Since the difference between the two partial dislocations is only the screw direction, these two dislocations induce equivalent elastic strain fields. In terms of elastic interaction, the difference between the two configurations would not affect the dopant distributions. In addition, preferential segregation is not seen -
along the {1120} stacking fault for all the kinds of dopants, although lattice defects could be preferential segregation sites. This is probably related to the structure of the stacking fault. Note that structure of the -
{11 2 0} stacking faults are equivalent regardless of the configurations of two partial dislocations, ACS Paragon Plus Environment
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whereas the 1/3 and 1/3 vectors are not equivalent due to the R3c symmetry of α-Al2O3 12, 14
-
-
-
. The {1120} stacking fault is formed on the cation sublattice, because the 1/3 (or 1/3) vector corresponds to a translation vector in the anion sublattice. This means that cations at the stacking fault as well as those in the bulk are located at the octahedral interstitial sites of the approximately close-packed oxygen ions, and thus the energy gain for cation segregation from the bulk to the stacking fault may be small. It was also found that all the kinds of dopants tend to segregate below the dislocation cores (i.e., the tensile strain region). This may be attributed to the strain effect. Since the dopants are cation, they should substitute Al sites. In the present cases, all kinds of the dopant cations have larger ionic radius than Al3+ (Table 1), and therefore the dopants should prefer to be distributed within tensile strain region below the dislocation cores to minimize the size-mismatch effect. In the Er3+-doped case (Figure 2d), the lower partial has the larger dopant distribution than the upper partial. Since Er+3 and Al3+ are the same ionic valence, the hydrostatic strain may be the dominant factor for the segregation. Then, the strain -
distribution of εxx (where the x direction refers the direction) were plotted around the partial dislocation cores, which is induced by their edge components17. Figure 3 illustrates the strain mapping of εxx in the present grain boundary calculated on the basis of the Peierls-Nabbaro model18, 19. The graph at the left-hand side shows the strain profile along the boundary. The size of the strain fields around the upper and lower partials significantly differs from each other due to the mutual elastic interaction from all the dislocations in the boundary. The tensile strain field of the upper partial is only the half of the separation distance of the pair, ~1.7 nm, whereas that of the lower partial is ~5.7 nm. The value of the tensile strain of the upper partial drops to zero more rapidly as seen in the left graph. The present results suggest that if the strain effect is a dominant factor, the dopant segregation should be more spread out in the lower partial than the upper partial. As already mentioned, the Er3+ case is in good agreement with this argument on the strain effect. Thus, we attribute the characteristic distribution of Er ions to the ACS Paragon Plus Environment
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asymmetric tensile strain fields of the partial pairs. It is noted that the upper partial has its tensile strain field bounded by the stacking fault, whereas the lower partial has its compressive strain field bounded by the stacking fault. Judging from the STEM observations, the distribution of Er ions is related to the strain fields, but not the presence of the stacking fault. This may be related to the atomic structure of the -
{1120} stacking fault as mentioned in the previous paragraph. The strain effect due to ionic size mismatches must contribute to all the kinds of dopants as in the Er3+-doped case. However, in the Sr2+- and Ni2+-doped cases (Figure 2b and 2c), the dopants tend to segregate more into the upper partials. Furthermore, the dopant distributions of Ni2+- and Zr4+-doped cases (Figure 2c and 2e) have different tendencies, although their ionic radii are very similar (Table 1). These results are inconsistent with the argument of the strain effect and thus additional effects need to be taken into account. In ionic crystal, the electrostatic effect may influence the segregation behavior. Considering the stoichiometry of each core of the undoped partial pair within the rigid model, the formal -
charge per the unit length along the dislocation line (|| = 8.25Å) is O-core: -3e (e: the elementary charge), Al1-core: 0, and Al2-core: +3e (Supplementary Discussion 2). To minimize the electrostatic energy, dopants are likely to segregate to compensate the core charges, depending on their valance state. When a dopant having a valence state less than 3+ occupy an Al3+ site, the dopant has a negative effective charge and is able to compensate a positive core charge (i.e., Al2-core). Conversely, a dopant having a valence state larger than 3+ is able to compensate a negative core charge (i.e., O-core). No electrostatic effect should act to the Al1-core because it is stoichiometric and thus electrically neutral. As mentioned, the previous (S)TEM studies give the inconsistent results on the core structures of the partials: the Al1-Al1 pair15 or the Al2-O pair9, and it has been reported that the energy difference between the two cases are very small22. In our observations, the upper partial tends to attract the divalent cations, whereas the lower partial tends to attract the tetravalent cations, which are in good agreement with the above argument on the electrostatic effect if the partial pair is assumed to have the Al2-O core structures. ACS Paragon Plus Environment
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Thus, it can be said that the impurity segregation to the dislocation cores in ionic crystals should be determined by the competition between the strain effect and electrostatic effect. In turn, our results support the formation of the nonstoichiometric partial cores of Al2-O type in the basal dislocations in αAl2O3. Although we have discussed the electrostatic interaction on dopant segregation within the rigid model so far, this may be a too simplified model. In actual cases, point defects such as interstitials or vacancies may be formed around the dislocation cores to compensate their charge unbalances to some extent. Nevertheless, our findings strongly suggest that not only the strain effect but also the electrostatic effect are needed to be taken into account to truly understand the point defect distributions including impurity ions around structural defects in ionic crystals. In conclusion, we directly observed asymmetric dopant segregation distributions at the basal dislocation cores in α-Al2O3. These results cannot be explained by the classical arguments on the strain effect but clearly demonstrate that the electrostatic effects, between charged dislocation cores and aliovalent impurity cations, have the strong effect on the impurity segregation behavior in ionic crystals. Our findings thus show a new important step towards the true understanding of the impurity-dislocation core interactions in complex, compound crystals.
ASSOCIATED CONTENT Supporting Information Supplementary Information is available.
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Determination of the dislocation core positions; formal charge of the 1/3 60o-partial dislocations in α-Al2O3 (PDF) ACS Paragon Plus Environment
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AUTHOR INFORMATION Corresponding Author *E-mail address:
[email protected] Notes The Authors declare no competing financial interests.
ACKNOWLEDGEMENTS A part of this study was supported by the Elements Strategy Initiative for Structural Materials (ESISM) from the Ministry of Education, Culture, Sports, Science, and Technology in Japan (MEXT), and a Grant-in-Aid for Scientific Research on Innovative Areas “Nano Informatics” (Grant No. 25106003) from Japan Society for the Promotion of Science (JSPS), “Nanotechnology Platform” (Project No. 12024046) of MEXT, Japan, and JSPS KAKENHI (Grant Nos. 15H02290, 15H04145 and 15K20959). The authors gratefully thank Dr. Okunishi for his help in part of our STEM observations.
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REFERENCES (1) Hirth, J. P.; Lothe, J. Theory of dislocations 2nd ed.; Krieger Publishing Company, Malabar, U.S.A., 1982. (2) Nakamura, A.; Matsunaga, K.; Tohma, J.; Yamamoto, T.; Ikuhara, Y. Nature Mater. 2003, 2, 453-456, DOI: 10.1038/nmat920. (3) Tokumoto, Y.; Amma, S.; Shibata, N.; Mizoguchi, T.; Edagawa, K.; Yamamoto, T.; Ikuhara, Y. J. Appl. Phys. 2009, 106, 124307, DOI: 10.1063/1.3270398. (4) Sugiyama, I.; Shibata, N.; Wang, Z.; Kobayashi, S.; Yamamoto, T.; Ikuhara, Y. Nature Nanotech. 2013, 8, 266-270, DOI: 10.1038/nnano.2013.45. (5) Cottrell, A. H.; Bilby, B. A. Proc. Phys. Soc. Section A 1949, 62, 49-62, DOI: 10.1088/03701298/62/1/308. (6) Blavette, D.; Cadel, E.; Fraczkiewicz, A.; Menand, A. Science 1999, 286, 2317-2319, DOI: 10.1126/science.286.5448.2317. (7) Thompson, K.; Flaitz, P. L.; Ronsheim, P.; Larson, D. J.; Kelly, T. F. Science 2007, 317, 1370-1374, DOI: 10.1126/science.1145428. (8) Whitworth, R. W. Adv. Phys. 1975, 24, 203-304, DOI: 10.1080/00018737500101401. (9) Shibata, N.; Chisholm, M. F.; Nakamura, A.; Pennycook, S. J.; Yamamoto, T.; Ikuhara Y. Science 2007, 316, 82-85, DOI: 10.1126/science.1136155. (10) Nakamura, A.; Matsunaga, K.; Yamamoto, T.; Ikuhara, Y. Philos. Mag. 2006, 86, 4657-4666, DOI: 10.1080/14786430600812820. (11) Shannon, R. D. Acta Cryst. Section A 1976, 32, 751-767, DOI: 10.1107/S0567739476001551. (12) Mitchell, T. E.; Pletka, B. J.; Phillips, D. S.; Heuer, A. H. Philos. Mag. 1976, 34, 441-451, DOI: 10.1080/14786437608222034. (13) Bilde-Sørensen, J. B.; Lawlor, B. F.; Geipel, T.; Pirouz, P.; Heuer, A. H.; Lagerlöf, K. P. D. Acta ACS Paragon Plus Environment
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Mater. 1996, 44, 2145-2152, DOI: 10.1016/1359-6454(95)00264-2. (14) Nakamura, A.; Yamamoto, T.; Ikuhara, Y. Acta Mater. 2002, 50, 101-108, DOI: 10.1016/S13596454(01)00318-4. (15) Heuer, A. H.; Jia, C. J.; Lagerlof, K. P. D. Science 2010, 330, 1227-1231, DOI: 10.1126/science.1192319 . (16) Pennycook, S. J.; Nellist, P. D. Scanning Transmission Electron Microscopy: Imaging and Analysis; Springer, New York, U.S.A., 2011. -
(17) The two partials are ±60o mixed-type dislocations and have parallel edge components of 1/6[1120] -
and antiparallel screw components of ±1/6[1100]. The screw components induce shear strain fields but do not affect the hydrostatic strain fields. (18) Peierls, R. Proc. Phys. Soc. 1940, 52, 34-37, DOI: 10.1088/0959-5309/52/1/305. (19) Nabarro, F. R. N. Proc. Phys. Soc. 1947, 59, 256-272, DOI: 10.1088/0959-5309/59/2/309. (20) Chung, D. H.; Simmons G. J. Appl. Phys. 1968, 39, 5316-5326, DOI: 10.1063/1.1655961. (21) Gieske J. H.; Barsch G. R. Phys. Stat. Sol. 1968, 29, 121-131, DOI: 10.1002/pssb.19680290113. (22) Tsuruta, K.; Tochigi, E.; Kezuka, Y.; Tanaka, K.; Shibata, N.; Nakamura, A.; Ikuhara Y. Acta Mater. 2014, 65, 76-84, DOI: 10.1016/j.actamat.2013.11.035.
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TABLE
Table 1 Atomic numbers, ionic valence and ionic radii of ions studied in this study. Ionic radii shown here are effective ionic radii of six-fold coordination based on the radius of
VI
O2- = 140 pm after Shannon11.
*The effective ionic radius of four-fold coordination. Sr
Ni
Er
Zr
Ti
Al
O
Atomic Number
38
28
68
40
22
13
8
Valence
2+
2+
3+
4+
4+
3+
2-
Ion Radius [pm]
118
69
89
72
60.5
53.5
138*
FIGURE CAPTIONS
Figure 1 -
Schematic illustrations showing rigid structure models of a 1/3 basal edge dislocation and partial dislocation cores in α-Al2O3. (a) A partial-dislocation pair dissociated by climb mechanism. The 1/3 and 1/3 partial dislocations lie on different basal planes with the {1120} stacking fault in between. (b) A partial dislocation terminated by oxygen column: O-core model. (c) terminated by single aluminum column: Al1-core model. (d) terminated by double aluminum column: Al2-core model.
Figure 2 HAADF STEM images of undoped and doped partial-dislocation pairs: (a) undoped, (b) Sr2+, (c) Ni2+, ACS Paragon Plus Environment
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(d) Er3+, (e) Zr4+, and (f) Ti4+. The red and blue spheres in (a) show the oxygen and aluminum columns, respectively. The positions of the partial dislocation cores are pointed by yellow arrows. The graphs below each STEM image show normalized image-intensity profiles along the horizontal direction. The blue and red profiles were obtained along the positions indicated by the blue and red triangles in the figures, respectively. The graphs in the bottom of the figures show the normalized image-intensity profiles along the horizontal direction. To obtain the profiles, STEM signals were summed up over the width of |1/6| (= 0.217nm) along the vertical direction and then normalized by the average value of the signals in the bulk.
Figure 3 -
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The color mapping showing elastic strain component, εxx, in the vicinity of the {1120}/ 2o grain boundary theoretically calculated by Peierls-Nabbaro model18, 19, where the shear modulus of 150 GPa20 and Poisson’s ratio of 0.2421 were used. The distances between the partial dislocations were taken from the experimental values and the partial dislocations were assumed to be located in line. The dislocation cores of the center partial pair are pointed by the arrows. The graph on the left-hand side shows the strain profile along the line in the map.
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Schematic illustrations showing rigid structure models of a 1/3 basal edge dislocation and partial dislocation cores in α-Al2O3. (a) A partial-dislocation pair dissociated by climb mechanism. The 1/3 and 1/3 partial dislocations lie on different basal planes with the {11-20} stacking fault in between. (b) A partial dislocation terminated by oxygen column: O-core model. (c) terminated by single aluminum column: Al1-core model. (d) terminated by double aluminum column: Al2-core model. 119x143mm (300 x 300 DPI)
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HAADF STEM images of undoped and doped partial-dislocation pairs: (a) undoped, (b) Sr, (c) Ni2+, (d) Er3+, (e) Zr4+, and (f) Ti4+. The red and blue spheres in (a) show the oxygen and aluminum columns, respectively. The positions of the partial dislocation cores are pointed by yellow arrows. The graphs below each STEM image show normalized image-intensity profiles along the horizontal direction. The blue and red profiles were obtained along the positions indicated by the blue and red triangles in the figures, respectively. The graphs in the bottom of the figures show the normalized image-intensity profiles along the horizontal direction. To obtain the profiles, STEM signals were summed up over the width of |1/6| (= 0.217nm) along the vertical direction and then normalized by the average value of the signals in the bulk. 119x186mm (300 x 300 DPI)
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The color mapping showing elastic strain component, εxx, in the vicinity of the {11-20}/ 2o grain boundary theoretically calculated by Peierls-Nabbaro model18, 19, where the shear modulus of 150 GPa20 and Poisson’s ratio of 0.2421 were used. The distances between the partial dislocations were taken from the experimental values and the partial dislocations were assumed to be located in line. The dislocation cores of the center partial pair are pointed by the arrows. The graph on the left-hand side shows the strain profile along the line in the map. 119x137mm (300 x 300 DPI)
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